write the equation of the line that contains the points (4,3) and (5,6)
To find the equation of a line that passes through two points, (x₁, y₁) and (x₂, y₂), we need to use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where:
- m is the slope of the line
- b is the y-intercept (the point where the line intersects the y-axis)
To find the slope (m), we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's apply this formula to the given points, (4,3) and (5,6).
x₁ = 4, y₁ = 3
x₂ = 5, y₂ = 6
m = (6 - 3) / (5 - 4)
m = 3 / 1
m = 3
Now that we have the slope, we can substitute it into the slope-intercept form along with the coordinates of one of the given points to find the value of b.
Using point (4,3):
3 = 3(4) + b
3 = 12 + b
b = 3 - 12
b = -9
Thus, the equation of the line that passes through the points (4,3) and (5,6) is:
y = 3x - 9